To solve the system of equations using the elimination method, we have the following system:
- \( 4x + 7y = 60 \)
- \( -4x + 7y = -4 \)
We can begin by adding both equations together to eliminate \( x \).
\[ (4x + 7y) + (-4x + 7y) = 60 + (-4) \]
This simplifies to:
\[ 0x + 14y = 56 \]
Thus, we have:
\[ 14y = 56 \]
Now, divide both sides by 14:
\[ y = 4 \]
Now that we have \( y \), we can substitute it back into one of the original equations to find \( x \). We'll use the first equation:
\[ 4x + 7(4) = 60 \]
This simplifies to:
\[ 4x + 28 = 60 \]
Subtract 28 from both sides:
\[ 4x = 32 \]
Now, divide both sides by 4:
\[ x = 8 \]
Therefore, the solution to the system of equations is \( (x, y) = (8, 4) \).
The correct ordered pair from the given options is:
(8, 4).